Numerical solution of algebraic Riccati equations by Newton's method

Author:

SIMA VASILEORCID,

Abstract

Improved Newton solvers, with or without line search, for both continuous- and discrete-time algebraic Riccati equations (AREs) are discussed. The basic theory and conceptual algorithm are briefly presented. Algorithmic details, computational steps, and convergence tests are described. The main results of an extensive performance investigation of the Newton solvers are summarized and compared with those obtained with the widelyused MATLAB solvers, care and dare. Randomly generated systems with orders till 2000, as well as the systems from the large COMPle ib collection of examples, are considered. Significantly improved accuracy, in terms of normalized and relative residuals, and sometimes greater efficiency than for care/dare have been obtained. The results strongly recommend the use of Newton solvers, especially for improving the solutions computed by other solvers.

Publisher

Academia de Stiinte Tehnice in Romania

Reference56 articles.

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